It is currently 24 Feb 2018, 17:35

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

The points A(0, 0), B(0, 4a - 5) and C(2a + 1, 2a + 6) form a triangle

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 43898
The points A(0, 0), B(0, 4a - 5) and C(2a + 1, 2a + 6) form a triangle [#permalink]

Show Tags

26 Mar 2015, 03:36
3
KUDOS
Expert's post
10
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

68% (02:16) correct 32% (02:37) wrong based on 180 sessions

HideShow timer Statistics

The points A(0, 0), B(0, 4a - 5) and C(2a + 1, 2a + 6) form a triangle. If angle ABC = 90, what is the area of triangle ABC?

A. 102
B. 120
C. 132
D. 144
E. 156

Kudos for a correct solution.
[Reveal] Spoiler: OA

_________________
Director
Joined: 07 Aug 2011
Posts: 578
GMAT 1: 630 Q49 V27
Re: The points A(0, 0), B(0, 4a - 5) and C(2a + 1, 2a + 6) form a triangle [#permalink]

Show Tags

26 Mar 2015, 05:01
2
KUDOS
1
This post was
BOOKMARKED
Bunuel wrote:
The points A(0, 0), B(0, 4a - 5) and C(2a + 1, 2a + 6) form a triangle. If angle ABC = 90, what is the area of triangle ABC?

A. 102
B. 120
C. 132
D. 144
E. 156

Kudos for a correct solution.

B and C should have same Y co-ordinate --> $$4a-5 = 2a+6$$ --> a=$$\frac{11}{2}$$

area of triangle = $$\frac{1}{2} * (4a-5) * (2a+1)$$ . on substituting a=$$\frac{11}{2}$$
we get area = 102 .

_________________

Thanks,
Lucky

_______________________________________________________
Kindly press the to appreciate my post !!

Retired Moderator
Status: On a mountain of skulls, in the castle of pain, I sit on a throne of blood.
Joined: 30 Jul 2013
Posts: 359
Re: The points A(0, 0), B(0, 4a - 5) and C(2a + 1, 2a + 6) form a triangle [#permalink]

Show Tags

26 Mar 2015, 06:14
2
KUDOS
1
This post was
BOOKMARKED
Bunuel wrote:
The points A(0, 0), B(0, 4a - 5) and C(2a + 1, 2a + 6) form a triangle. If angle ABC = 90, what is the area of triangle ABC?

A. 102
B. 120
C. 132
D. 144
E. 156

Kudos for a correct solution.

1/2bh=1/2(2a+1)(2a+6)

Now 4a-5=2a+6
2a=11

Therefore,
A(0,0); B(0,17); C(12,17)

1/2*17*12=102

Math Expert
Joined: 02 Sep 2009
Posts: 43898
Re: The points A(0, 0), B(0, 4a - 5) and C(2a + 1, 2a + 6) form a triangle [#permalink]

Show Tags

30 Mar 2015, 02:37
3
KUDOS
Expert's post
1
This post was
BOOKMARKED
Bunuel wrote:
The points A(0, 0), B(0, 4a - 5) and C(2a + 1, 2a + 6) form a triangle. If angle ABC = 90, what is the area of triangle ABC?

A. 102
B. 120
C. 132
D. 144
E. 156

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:
Attachment:

righttrianglearea_text.PNG [ 17.63 KiB | Viewed 4711 times ]

_________________
Intern
Joined: 05 Aug 2016
Posts: 1
Re: The points A(0, 0), B(0, 4a - 5) and C(2a + 1, 2a + 6) form a triangle [#permalink]

Show Tags

12 Jan 2018, 11:22
AmoyV wrote:
Bunuel wrote:
The points A(0, 0), B(0, 4a - 5) and C(2a + 1, 2a + 6) form a triangle. If angle ABC = 90, what is the area of triangle ABC?

Now 4a-5=2a+6

Sorry, but I did not get to your calculations - why it is so? What I missed?
Intern
Joined: 12 Dec 2017
Posts: 3
The points A(0, 0), B(0, 4a - 5) and C(2a + 1, 2a + 6) form a triangle [#permalink]

Show Tags

19 Jan 2018, 01:13
1
KUDOS
Aksena wrote:
AmoyV wrote:
Bunuel wrote:
The points A(0, 0), B(0, 4a - 5) and C(2a + 1, 2a + 6) form a triangle. If angle ABC = 90, what is the area of triangle ABC?

Now 4a-5=2a+6

Sorry, but I did not get to your calculations - why it is so? What I missed?

Im guessing you have problems understanding why 4a-5 = 2a+6

Now, the reason they got to that equation was due to the given information that angle ABC = 90
--> This implies that triangle ABC was a right angle
--> Now A was given at the origin (0,0), while B was given to be somewhere along the Y-axis as its X-coordinates = 0
--> Hence, as ABC was a right triangle, the point C will have the same Y-coordinates as B in order to form the right triangle (i.e. to fulfill angle ABC = 90)
--> B(0,4a-5) and C(2a+1, 2a+6)
--> Therefore 4a-5 = 2a+6, solve for a and you can find the area of the triangle with the basic area formula for right triangles: base x height / 2
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2192
Location: United States (CA)
Re: The points A(0, 0), B(0, 4a - 5) and C(2a + 1, 2a + 6) form a triangle [#permalink]

Show Tags

21 Jan 2018, 18:33
Bunuel wrote:
The points A(0, 0), B(0, 4a - 5) and C(2a + 1, 2a + 6) form a triangle. If angle ABC = 90, what is the area of triangle ABC?

A. 102
B. 120
C. 132
D. 144
E. 156

Since we have a right triangle with angle ABC = 90, we see that vertices A and B share the same x-coordinate, and vertices B and C share the same y-coordinate.

Equating the y-coordinates of vertices B and C, we have:

4a - 5 = 2a + 6

2a = 11

a = 5.5

Substituting 5.5 for a, we see that the ordered pair for vertex B is (0, 4(5.5) - 5), or (0, 17). Thus, leg AB is the vertical distance from (0,0) to (0,17), or 17.
Similarly, we see that the ordered pair for vertex C is (12, 17) and leg BC is is the horizontal distance from (0,17) to (12, 17) = 12.

Thus, the area of the triangle is:

area = base x height x 1/2

area = 17 x 12 x 1/2 = 17 x 6 = 102

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: The points A(0, 0), B(0, 4a - 5) and C(2a + 1, 2a + 6) form a triangle   [#permalink] 21 Jan 2018, 18:33
Display posts from previous: Sort by